10.4 Calculations with Odds and Logit

Our goal in utilizing logistic regression is to identify the probability of an instance belonging to a class of interest.

Logistic regression produces logit, that is, z.

To find the Odds that something will happen, raise e to the power of logit:

Natural Logarithms

The symbol e represents the base for a natural logarithm. That is, e = 2.718281828459

The image below demonstrates the relationship between taking a natural log, and taking the inverse of a natural log.

In continuing our example about the odds of having a second heart attack, consider that the odds are 7:4, or 1.75. What is logit?

If the data mining software produces a value of 0.55962 for logit, what are the odds of second heart attack?

How Values of logit Influences Odds and Probability

The image below shows what the Odds are for different values of z. When z = 0, Odds = 1. Having a value of 1 for Odds means that we are just as likely to see a success as we are to see a failure. (Recall that Odds = successes : failures so odds of 1 = 1:1). When Odds = 1, Probability = .5. In other words the probability of success 50%.

The base of natural logarithms is e = 2.718, so, in the chart below, to get Odds we raise 2.718 to the power of z.

Anything raised to the power of 1 results in itself, so for e¹ = 2.718.

Practice with logit, odds, and probability

The following video discusses taking the natural log, and the inverse of the natural log to calculate logit and Odds. Please watch it and come to class prepared with any questions you have.